What is the value of the ones digit in the solution to ...

Question

help!!!! · Answer

$$2^{326}$$

help!!!! · Answer

How would I solve this??

help!!!! · Answer

The answer is 4...

mathmale · Answer

The only addition involved here is addition of the exponents.
$$2^{326}=2^{300}2^{20}2^6$$

photon336 · Answer

I see

mathmale · Answer

I suggest you try to find a relationship that correctly predicts the final digit of any given positive power of 2.

For example, if n=1, 2^n=2  
If n=2, 2^n=4
If n=3, 2^n=8
             2^4=16
             2^5=32
              2^6=64
....
             2^10 = 1024

According to this experiment, the final digit is 4 when n=2, 6, 10, 14, 18, and so on

Take this idea and run with it.  Can you predict what the final digit will be if n=326?

help!!!! · Answer

hmm I'm kind of lost here. I get your experiment but I don't know how to apply to the problem

help!!!! · Answer

If I plug 326 for my n, I get 1.36....

help!!!! · Answer

2^326=1.36E98

bobo-i-bo · Answer

So basically, finding the first digit of 2^326 is to find 2^326 mod 10. Do you know the laws of modular arithmetic?